Finite Group Databasebeta

← #479×D97 #27151509

Subgroups — #479×D97 #27151509

Order 12416.

384 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×D97C211yesmaximal, characteristic
2C4×Q8×D97C211yesmaximal, characteristic
3#20261045C211yesmaximal, characteristic, complemented
4#20261044C211yesmaximal, characteristic, complemented
5#20261043C211yesmaximal, characteristic, complemented
6#20261042C211yesmaximal, characteristic, complemented
7#20261041C211yesmaximal, characteristic, complemented
8#20261040C211yesmaximal, characteristic, complemented
9#20261039C211yesmaximal, characteristic, complemented
10#107×D97C211yesmaximal, characteristic
11#106×D97C211yesmaximal, characteristic
12C4⋊C8×D97C211yesmaximal, characteristic
13#103×D97C211yesmaximal, characteristic
14#103×D97C211yesmaximal, characteristic
15#479×C97C211yesmaximal, characteristic, complemented
16C2×Q8×D97C2211yescharacteristic
17C2×C8×D97C2211yescharacteristic
18C2×C8×D97C2211yescharacteristic
19#15690802C2211yescharacteristic
20#15690801C2211yescharacteristic
21#15690801C2211yescharacteristic
22#15690800—21no—
23#15690800—21no—
24Q8×Dic97C2211yescharacteristic
25C4×Dic194—21no—
26C4×Dic194C2211yescharacteristic
27#15690775—21no—
28#15690775C2211yescharacteristic
29C4⋊C4×D97—21no—
30C4⋊C4×D97—21no—
31C4⋊C4×D97—21no—
32C4⋊C4×D97C2211yescharacteristic
33C4⋊C4×D97C2211yescharacteristic
34C4⋊C4×D97C2211yescharacteristic
35C42×D97—21no—
36C42×D97C2211yescharacteristic
37#15690744C2211yescharacteristic
38#15690743C2211yescharacteristic
39#15690743C2211yescharacteristic
40#15690742C2211yescharacteristic
41#15690741C2211yescharacteristic
42#15690741C2211yescharacteristic
43C4⋊#11715895C2211yescharacteristic
44#15690739C2211yescharacteristic
45#15690739C2211yescharacteristic
46#15690735C2211yescharacteristic
47#15690735C2211yescharacteristic
48#15690734C2211yescharacteristic
49#15690734C2211yescharacteristic
50#15690733C2211yescharacteristic
51#15690733C2211yescharacteristic
52#125×C97C2211yescharacteristic
53C4×Q8×C97C2211yescharacteristic
54#107×C97C2211yescharacteristic
55#106×C97C2211yescharacteristic
56C4⋊C8×C97C2211yescharacteristic
57#103×C97C2211yescharacteristic
58#103×C97C2211yescharacteristic
59C2×Dic194—21no—
60C2×Dic194C2311yescharacteristic
61Q8×D97—22no—
62Q8×D97Q814yes—
63C2×C4×D97—21no—
64C2×C4×D97—21no—
65C2×C4×D97—21no—
66C2×C4×D97—21no—
67C2×C4×D97D411yescharacteristic
68C2×C4×D97D411yescharacteristic
69C2×C4×D97C2311yescharacteristic
70C2×#11715895C2311yescharacteristic
71C2×#11715895C2311yescharacteristic
72C8×D97—22no—
73C8×D97—22no—
74C4⋊Dic97—21no—
75C4⋊Dic97—21no—
76C4⋊Dic97—21no—
77C4⋊Dic97C2311yescharacteristic
78C4⋊Dic97C2311yescharacteristic
79C4⋊Dic97C2311yescharacteristic
80#13095490—21no—
81#13095490—21no—
82#13095490—21no—
83#13095490—21no—
84#13095490—21no—
85#13095490—21no—
86#13095490—21no—
87#13095490—21no—
88#13095490—21no—
89C4×Dic97—21no—
90C4×Dic97—21no—
91C4×Dic97—21no—
92C4×Dic97D411yescharacteristic
93C4×Dic97D411yescharacteristic
94C4×Dic97C2311yescharacteristic
95C2×Q8×C97C2311yescharacteristic
96C2×C8×C97C2311yescharacteristic
97C2×C8×C97C2311yescharacteristic
98C4⋊C4×C97—21no—
99C4⋊C4×C97—21no—
100C4⋊C4×C97—21no—
101C4⋊C4×C97C2311yescharacteristic
102C4⋊C4×C97C2311yescharacteristic
103C4⋊C4×C97C2311yescharacteristic
104C42×C97—21no—
105C42×C97C2311yescharacteristic
106C22×D97C2×D411yescharacteristic
107Q8×C97—21no—
108Q8×C97C2×Q812yes—
109C2×C4×C97—21no—
110C2×C4×C97—21no—
111C2×C4×C97—21no—
112C2×C4×C97—21no—
113C2×C4×C97C2×D411yescharacteristic
114C2×C4×C97C2×D411yescharacteristic
115C2×C4×C97C2411yescharacteristic
116C2×Dic97—21no—
117C2×Dic97—21no—
118C2×Dic97—21no—
119C2×Dic97—21no—
120C2×Dic97C2×D411yescharacteristic
121C2×Dic97C2×D411yescharacteristic
122C2×Dic97C2×D411yescharacteristic
123C4×D97—24no—
124C4×D97—22no—
125C4×D97—22no—
126C4×D97—42no—
127C4×D97—42no—
128C4×D97—42no—
129C4×D97C2×Q812yes—
130C4×D97#4112yes—
131Dic194—21no—
132Dic194—24no—
133Dic194C2×Q812yes—
134C8×C97—21no—
135C8×C97—21no—
136#11715895—21no—
137#11715895—21no—
138C22×C97C22×D411yescharacteristic
139C2×D97C22⋊Q812yes—
140C2×D97#13512yes—
141C2×D97#13712yes—
142C4×C97—22no—
143C4×C97—21no—
144C4×C97—21no—
145C4×C97—41no—
146C4×C97—41no—
147C4×C97—41no—
148C4×C97C22×Q811yescharacteristic
149C4×C97C2×#4111yescharacteristic
150Dic97—22no—
151Dic97—21no—
152Dic97—21no—
153Dic97—41no—
154Dic97—41no—
155Dic97—41no—
156Dic97C22⋊Q812yes—
157C2×C97C2×C22⋊Q811yescharacteristic
158C2×C97C2×#13511yescharacteristic
159C2×C97C2×#13711yescharacteristic
160D97#47914yesdirect product factor
161C2×#479—971nomaximal, Sylow
162C97C2×#47911yescharacteristic, complemented, Sylow
163C2×#125—971no—
164C2×C4×Q8—971no—
165#479—971no—
166#479—971no—
167#479—971no—
168#479—971no—
169#479—971no—
170#479—971no—
171#479—971no—
172#479D9711yescharacteristic, direct product factor
173C2×#107—971no—
174C2×#106—971no—
175C2×C4⋊C8—971no—
176C2×#103—971no—
177C2×#103—971no—
178C22×Q8—971no—
179C22×C8—971no—
180C22×C8—971no—
181#125—971no—
182#125—971no—
183#125—971no—
184#125—1941no—
185#125—1941no—
186#125C2×D9711yescharacteristic
187C4×Q8—971no—
188C4×Q8—971no—
189C4×Q8—971no—
190C4×Q8—1941no—
191C4×Q8—1941no—
192C4×Q8C2×D9711yescharacteristic
193C2×C4⋊C4—971no—
194C2×C4⋊C4—971no—
195C2×C4⋊C4—971no—
196C2×C4⋊C4—1941no—
197C2×C4⋊C4—1941no—
198C2×C4⋊C4—1941no—
199C2×C42—971no—
200C2×C42—1941no—
201#107—971no—
202#107—971no—
203#107—971no—
204#107C2×D9711yescharacteristic
205#106—971no—
206#106—971no—
207#106—971no—
208#106C2×D9711yescharacteristic
209C4⋊C8—971no—
210C4⋊C8—971no—
211C4⋊C8—971no—
212C4⋊C8C2×D9711yescharacteristic
213#103—971no—
214#103—971no—
215#103—971no—
216#103—971no—
217#103—971no—
218#103—971no—
219#103C2×D9711yescharacteristic
220#103C2×D9711yescharacteristic
221C2×Q8—974no—
222C2×Q8—971no—
223C2×Q8—1941no—
224C2×Q8—1942no—
225C2×Q8C22×D9711yescharacteristic
226C22×C4—971no—
227C22×C4—971no—
228C22×C4—971no—
229C22×C4—1941no—
230C22×C4—1941no—
231C22×C4—1941no—
232C22×C4—1941no—
233C2×C8—971no—
234C2×C8—971no—
235C2×C8—1942no—
236C2×C8—1942no—
237C2×C8C22×D9711yescharacteristic
238C2×C8C22×D9711yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—971no—
243C4⋊C4—971no—
244C4⋊C4—971no—
245C4⋊C4—1941no—
246C4⋊C4—1941no—
247C4⋊C4—1941no—
248C4⋊C4—1941no—
249C4⋊C4—1941no—
250C4⋊C4—1941no—
251C4⋊C4—1941no—
252C4⋊C4—1941no—
253C4⋊C4—1941no—
254C4⋊C4—1941no—
255C4⋊C4—1941no—
256C4⋊C4—1941no—
257C4⋊C4C22×D9711yescharacteristic
258C4⋊C4C22×D9711yescharacteristic
259C4⋊C4C22×D9711yescharacteristic
260C42—21no—
261C42—971no—
262C42—971no—
263C42—971no—
264C42—1941no—
265C42—1941no—
266C42—1941no—
267C42C22×D9711yescharacteristic
268C23—971no—
269Q8—21no—
270Q8—972no—
271Q8—1944no—
272Q8—1941no—
273Q8Q8×D9712yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—971no—
279C2×C4—972no—
280C2×C4—972no—
281C2×C4—971no—
282C2×C4—971no—
283C2×C4—3882no—
284C2×C4—3882no—
285C2×C4—3882no—
286C2×C4—1942no—
287C2×C4—1942no—
288C2×C4—1944no—
289C2×C4—1941no—
290C2×C4—1941no—
291C2×C4—1941no—
292C2×C4—1941no—
293C2×C4D4×D9711yescharacteristic
294C2×C4D4×D9711yescharacteristic
295C2×C4C23×D9711yescharacteristic
296C8—21no—
297C8—21no—
298C8—1941no—
299C8—1941no—
300C22—972no—
301C22—972no—
302C22—972no—
303C22C2×D4×D9711yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—972no—
311C4—3881no—
312C4—3881no—
313C4—3881no—
314C4—1942no—
315C4—1941no—
316C4—1941no—
317C4C2×Q8×D9711yescharacteristic
318C4#41×D9711yescharacteristic
319C2—974no—
320C2C22⋊Q8×D9711yescharacteristic
321C2#135×D9711yescharacteristic
322C2#137×D9711yescharacteristic
subgroupG/H
centerC22C2×D4×D97
commutator, cosocleC2×C4×C97C24
FrattiniC2×C4C23×D97
Fitting#479×C97C2
socleC22×C97C22×D4
prime radicalC22×D97C2×D4
hypercenter#479D97
hypocenterC97C2×#479
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #20261045C2semidirect
4. #20261044C2semidirect
5. #20261043C2semidirect
6. #20261042C2semidirect
7. #20261041C2semidirect
8. #20261040C2semidirect
9. #20261039C2semidirect
15. #479×C97C2semidirect
160. D97#479direct (N × H)
162. C97C2×#479semidirect
172. #479D97direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#125×D972
C4×Q8×D972
#202610452
#202610442
#202610432
#202610422
#202610412
#202610402
#202610392
#107×D972
#106×D972
C4⋊C8×D972
#103×D972
#479×C972
C2×#47997